Download presentation

Presentation is loading. Please wait.

Published byNikhil Nute Modified over 4 years ago

1
Number Systems

2
Common Number Systems SystemBaseSymbols Used by humans? Used in computers? Decimal100, 1, … 9YesNo Binary20, 1NoYes Octal80, 1, … 7No Hexa- decimal 160, 1, … 9, A, B, … F No

3
Quantities/Counting (1 of 3) DecimalBinaryOctal Hexa- decimal 0000 1111 21022 31133 410044 510155 611066 711177 p. 33

4
Quantities/Counting (2 of 3) DecimalBinaryOctal Hexa- decimal 81000108 91001119 10101012A 11101113B 12110014C 13110115D 14111016E 15111117F

5
Quantities/Counting (3 of 3) DecimalBinaryOctal Hexa- decimal 16100002010 17100012111 18100102212 19100112313 20101002414 21101012515 22101102616 23101112717 Etc.

6
Conversion Among Bases The possibilities: Hexadecimal DecimalOctal Binary pp. 40-46

7
Quick Example 25 10 = 11001 2 = 31 8 = 19 16 Base

8
Decimal to Decimal (just for fun) Hexadecimal DecimalOctal Binary Next slide…

9
125 10 =>5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight

10
Binary to Decimal Hexadecimal DecimalOctal Binary

11
Binary to Decimal Technique –Multiply each bit by 2 n, where n is the weight of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results

12
Example 101011 2 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = 32 43 10 Bit 0

13
Octal to Decimal Hexadecimal DecimalOctal Binary

14
Octal to Decimal Technique –Multiply each bit by 8 n, where n is the weight of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results

15
Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10

16
Hexadecimal to Decimal Hexadecimal DecimalOctal Binary

17
Hexadecimal to Decimal Technique –Multiply each bit by 16 n, where n is the weight of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results

18
Example ABC 16 =>C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 = 2560 2748 10

19
Decimal to Binary Hexadecimal DecimalOctal Binary

20
Decimal to Binary Technique –Divide by two, keep track of the remainder –First remainder is bit 0 (LSB, least-significant bit) –Second remainder is bit 1 –Etc.

21
Example 125 10 = ? 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1 125 10 = 1111101 2

22
Octal to Binary Hexadecimal DecimalOctal Binary

23
Octal to Binary Technique –Convert each octal digit to a 3-bit equivalent binary representation

24
Example 705 8 = ? 2 7 0 5 111 000 101 705 8 = 111000101 2

25
Hexadecimal to Binary Hexadecimal DecimalOctal Binary

26
Hexadecimal to Binary Technique –Convert each hexadecimal digit to a 4-bit equivalent binary representation

27
Example 10AF 16 = ? 2 1 0 A F 0001 0000 1010 1111 10AF 16 = 0001000010101111 2

28
Decimal to Octal Hexadecimal DecimalOctal Binary

29
Decimal to Octal Technique –Divide by 8 –Keep track of the remainder

30
Example 1234 10 = ? 8 8 1234 154 2 8 19 2 8 2 3 8 0 2 1234 10 = 2322 8

31
Decimal to Hexadecimal Hexadecimal DecimalOctal Binary

32
Decimal to Hexadecimal Technique –Divide by 16 –Keep track of the remainder

33
Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4

34
Binary to Octal Hexadecimal DecimalOctal Binary

35
Binary to Octal Technique –Group bits in threes, starting on right –Convert to octal digits

36
Example 1011010111 2 = ? 8 1 011 010 111 1 3 2 7 1011010111 2 = 1327 8

37
Binary to Hexadecimal Hexadecimal DecimalOctal Binary

38
Binary to Hexadecimal Technique –Group bits in fours, starting on right –Convert to hexadecimal digits

39
Example 1010111011 2 = ? 16 10 1011 1011 2 B B 1010111011 2 = 2BB 16

40
Octal to Hexadecimal Hexadecimal DecimalOctal Binary

41
Octal to Hexadecimal Technique –Use binary as an intermediary

42
Example 1076 8 = ? 16 1 0 7 6 001 000 111 110 2 3 E 1076 8 = 23E 16

43
Hexadecimal to Octal Hexadecimal DecimalOctal Binary

44
Hexadecimal to Octal Technique –Use binary as an intermediary

45
Example 1F0C 16 = ? 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4 1F0C 16 = 17414 8

46
Exercise – Convert... Dont use a calculator! DecimalBinaryOctal Hexa- decimal 33 1110101 703 1AF Skip answer Answer

47
Exercise – Convert … DecimalBinaryOctal Hexa- decimal 331000014121 117111010116575 4511110000117031C3 4311101011116571AF Answer

48
Binary Addition (1 of 2) Two 1-bit values ABA + B 000 011 101 1110 two

49
Binary Addition (2 of 2) Two n-bit values –Add individual bits –Propagate carries –E.g., 10101 21 + 11001 + 25 101110 46 11

50
Multiplication (1 of 2) Binary, two 1-bit values AB A B 000 010 100 111

51
Multiplication (2 of 2) Binary, two n-bit values –As with decimal values –E.g., 1110 x 1011 1110 1110 0000 1110 10011010

52
Thank you

Similar presentations

OK

IT101: INFORMATION TECHNOLOGY FUNDAMENTALS 1 Edited By Dr. Ahmed Abo-Bakr Information Technology Dept. Faculty of Computers & Information.

IT101: INFORMATION TECHNOLOGY FUNDAMENTALS 1 Edited By Dr. Ahmed Abo-Bakr Information Technology Dept. Faculty of Computers & Information.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on psu in india Ppt on latest technology Ppt on video teleconferencing system Perfect competition long run ppt on tv Ppt on charles dickens and his life Ppt on wild animals for grade 1 Ppt on bluetooth based smart sensor networks applications Ppt on grease lubrication in rolling Ppt on object-oriented programming php Ppt on life history of mahatma gandhi